Brand loyalty does not an objective consumer make.
In the last generation ATI had driver problems and Nvidia had some badly designed video cards. At this stage both manufacturers have improved these issues.
HD 6970 = GTX 570
http://www.hwcompare.com/9020/geforce-gtx-570-vs-radeon-hd-6970/
HD 6950 = GTX 560 Ti
http://www.hwcompare.com/8888/geforce-gtx-560-ti-vs-radeon-hd-6950-2gb/
HD 6870 = GTX 470
http://www.hwcompare.com/8627/geforce-gtx-470-vs-radeon-hd-6870/
At this time there are no distinct performance advantages between the brands.
I keep reading in forums that the HD 6950 pwns the GTX 560 Ti, but when I've looked at pretty much any benchmark the performance between the two is typically within a margin of error that would not be distinguishable by the human eye (1 to 3 frames).
Basically if your price range is under $200, you go and look at the HD 6950, GTX 560 Ti, HD 6970, GTX 470, HD 5870, HD 6870 and which ever one is on sale for $125 to $150, you buy that one.